References - Bogoliubov Laboratory of Theoretical Physics - JINR

account their RG evolution. As a result, we extract the value of the singlet axial charge
a0(1 GeV 2 ) = 0.33 ± 0.05. This value is very close to the corresponding COMPASS
0.35 ± 0.06 [7] and HERMES 0.35 ± 0.06 [8] results.
Table 1: Combined fit results of the proton Γ p
1 (Q2 ) data (elastic contribution excluded). APT fit results a0
AP T and μ4,6,8 (at the scale Q2 0 =1GeV2 ) are given without and with taking into account the RG Q2-evolution of
a0(Q2 AP T ) and μ4 (Q2 ). The minimal borders of fitting domains in Q2 are settled from the ad hoc restriction
χ2 � 1 and monotonous behavior of the resulting fitted curves.
Method Q 2 min, GeV 2
a0 μ4/M 2 μ6/M 4 μ8/M 6
0.59 0.33(3) −0.050(4) 0 0
PT 0.35 0.43(5) −0.087(9) 0.024(5) 0
0.29 0.37(5) −0.060(15) -0.001(8) 0.006(5)
0.47 0.35(4) −0.054(4) 0 0
APT 0.17 0.39(3) −0.069(4) 0.0081(8) 0
(no evolution) 0.10 0.43(3) −0.078(4) 0.0132(9) −0.0007(5)
0.47 0.33(4) −0.051(4) 0 0
APT 0.17 0.31(3) −0.059(4) 0.0098(8) 0
(with evolution) 0.10 0.32(4) −0.065(4) 0.0146(9) −0.0006(5)
In order to see how the Q2 min scale and fit results for the μ-terms change with varying
ΛQCD, we have performed three different NLO fits with ΛQCD = 300, 400, 500 MeV. It
turns out that the term μ4 is quite sensitive to the Landau singularity position, and its
value noticeably increases with increasing ΛQCD. The APT is free of such a problem
thus providing a reliable tool of investigating the behavior of higher twist terms extracted
directly from the low-energy data.
In the APT approach the convergence of both the higher orders and higher twist series
is much better. In both the nonsinglet and singlet case, while the twist-4 term happened
to be larger in magnitude in the APT than in the conventional PT, the subsequent
terms are essentially smaller and quickly decreasing (as the APT absorbs some part of
nonperturbative dynamics described by higher twists). This is the main reason of the
shift of the pQCD frontier to lower Q values. A satisfactory description of the proton
spin sum rule data down to Q ∼ ΛQCD � 350 MeV was achieved (see Fig. 1b). In a
sense, this could be natural if the main reason of such a success was the disappearance of
unphysical singularities. Note that the data at very low Q ∼ ΛQCD are usually dropped
from the analysis of a0 and higher-twist term in the standard PT analysis because of
Landau singularities. The compatibility of our results for a0 and previous results [7, 8]
demonstrates the universality of the nucleon spin structure at large and low Q2 scales.
This work was partially supported by RFBR grants 07-02-91557, 08-01-00686, 08-
02-00896-a, and 09-02-66732, the JINR-Belorussian Grant (contract F08D-001) and RF
Scientific School grant 1027.2008.2.
References
[1] S.E. Kuhn, J.P. Chen and E. Leader, Prog. Part. Nucl. Phys. 63 (2009) 1.
100